Back about 15 years a go I had 2 sons working for Delta, I was also PM with them at the time so I had complementary Crown Room membership. Not only did Non Rev passengers have to "dress up" and I do believe a dog or cat could have bumped me off a flight but in addition I found out the hard way that "employees and non-rev passengers" were not allowed to use the Crown Room as I was unceremoniously told I had to leave the CVG CR while connecting on a non rev trip. So Delta does have some history in having and enforcing a dress code on employees when they were flying. Now with that said I personally could not care less what anyone wears on the plane, rev or non-rev alike, to many things way higher than that on my "important meter" YMMV!